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Proceedings of the American Mathematical Society

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Compact perturbations of $m$-accretive operators in Banach spaces


Author: Claudio H. Morales
Journal: Proc. Amer. Math. Soc. 134 (2006), 365-370
MSC (2000): Primary 47H10
DOI: https://doi.org/10.1090/S0002-9939-05-08343-7
Published electronically: September 20, 2005
MathSciNet review: 2176003
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Abstract: This paper continues a discussion that arose twenty years ago, concerning the perturbation of an $m$-accretive operator by a compact mapping in Banach spaces. Indeed, if $A$ is $m$-accretive and $g$ is compact, then the boundary condition $tx \notin A(x)g(x)$ for $x \in \partial G \cap D(A)$ and $t<0$ implies that $0$ is in the closure of the range of $A+g$. Perhaps the most interesting aspect of this result is the proof itself, which does not appeal to the classical degree theory argument used for this type of problem.


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Additional Information

Claudio H. Morales
Affiliation: Department of Mathematics, University of Alabama in Huntsville, Huntsville, Alabama 35899

DOI: https://doi.org/10.1090/S0002-9939-05-08343-7
Keywords: $m$-accretive operators, pseudo-contractive and compact operators
Received by editor(s): February 5, 2004
Published electronically: September 20, 2005
Communicated by: Jonathan M. Borwein
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.